Nonparametric Identification for Respondent-Driven Sampling

TL;DR

This paper provides nonparametric identification conditions for respondent-driven sampling (RDS), clarifying when the popular Volz-Heckathorn estimator is consistent without requiring random sampling or a connected network.

Contribution

It establishes general conditions under which the population mean can be identified in RDS, expanding the understanding of estimator validity beyond previous assumptions.

Findings

Conditions for the consistency of the VH estimator are less restrictive than previously thought.

Identification of population means does not require a fully connected social network.

The results do not depend on random sampling assumptions.

Abstract

Respondent-driven sampling is a survey method for hidden or hard-to-reach populations in which sampled individuals recruit others in the study population via their social links. The most popular estimator for for the population mean assumes that individual sampling probabilities are proportional to each subject's reported degree in a social network connecting members of the hidden population. However, it remains unclear under what circumstances these estimators are valid, and what assumptions are formally required to identify population quantities. In this short note we detail nonparametric identification results for the population mean when the sampling probability is assumed to be a function of network degree known to scale. Importantly, we establish general conditions for the consistency of the popular Volz-Heckathorn (VH) estimator. Our results imply that the conditions for consistency of the VH estimator are far less stringent than those suggested by recent work on diagnostics for RDS. In particular, our results do not require random sampling or the existence of a network connecting the population.